SURGE FORMATION IN OPEN CHANNELS IN RELATION TO THE DURATION OF GATE OPERATIONS

 

Friedrich SCHÖBERL

 

A.Univ.Prof. Dr. Dipl.-Ing., Institut für Wasserbau, Innsbruck University Technikerstraße 13, A-6020 Innsbruck, Austria, Phone ++43-512 507 6950;

Fax ++43-512 507 2912; E-mail f.schoe@uibk.ac.at

 

 

ABSTRACT

Surges in open channels have been studied to evaluate the effect of gate closing time on the wave formation. Dependent on the duration of operation, different surge patterns can be observed, considerably influencing the resulting water elevation. Compared to theoretical calculations the performed measurements provide improved insight and allow the application of diagrams to assess relevant surge characteristics.

 

Keywords: surge classification, time effect of gate closure, surge height characteristics

 

INTRODUCTION

Surges appear as sudden elevations of the water level caused by rapidly varying discharges. Such phenomena play an important part in the design of hydraulic structures as navigation canals and tail race or head race channels of electric power plants. There they determine the necessary height of banks and the layout of profiles. The following investigation was caused by questions about the impact of emergency closure operations of a run of the river plant. Operational constraints can require the optional closure of turbines within 3 to 10 seconds. The investigations concentrated on the positive surge formation on the upstream side of the channel.

Surges do not always assume a unity of shape. Usually two main forms are distinguished: a wave formation similar to a bore which can be identified as a ventilated hydraulic jump and a wave where the front splits up in a series of oscillations. An easy theoretical treatment becomes possible by applying the momentum and continuity equation to a co-ordinate system moving together with the wave front and presuming a monoclinal shape. In dimensionless form this relation

 

reads Eq.1

 

with and , where z_S is the resulting surge height, h_O the initial water depth, v_O the initial flow velocity and g the acceleration due to gravity. With respect to Eq. 1 the surge height z_S* proves to be a function of the Froude number F_O only. The computation does not account for differences of the surge regime. According to Favre (1935) a bore will initiate if Eq.2

Since oscillating surges produce considerably larger water level elevations than bores, an extension of the approach in Eq.1 becomes necessary. Introducing the effect of the vertical flow velocity component, the theoretical analysis reveals

Eq.3

where z_OS denotes the maximum computed peak of an oscillating surge, see Martin (1990). In no case the calculations explicitly consider the effect of closure time. So it remains unclear what "rapidly" in terms of the change of velocity or discharge quantitatively means. The study tries to prove the impact of different lengths of gate closure and to quantify how the gate manipulations affect the features of the surge wave.

 

EXPERIMENTAL ANALYSIS

 

TEST CONDITIONS

The tests were carried out in a 0,3 m wide, 0,5 m high and 6 m long rectangular flume equipped with two sluice gates at the downstream end. One gate regulated the initial water level and the second gate was used for closing operations. The surge was produced by lowering this gate within different time spans between 0,1 and 10 seconds. In the test runs the channel slope varied in a range between 0,05 to 1 % to cover a wide spectrum of wave types and allow for the determination of the thresholds between the different wave formations. Uniform flow was regulated for discharges varying between 5 and 30 l/s. To monitor the propagation of the surge to a recorder. In addition, the surge advancement was filmed by a video camera. The main tests were performed by fully closing the gate.

 

TIME SPECIFIC SURGE PARAMETERS

Characterising the temporal behaviour of a surge, different elevation parameters are of interest, see fig.1: z₁ as first peak of the surge, not necessarily identical with z_max

the maximum amplitude of the surge and z_m the mean surge height. Since the upstream advancement of a surge in an inclined channel leads to a continuous rise of the surge depth, it is necessary to separate this additional effect by taking into account the mean elevation time t_{Z mean}.

 

 

Fig.1 schematic time graph of a surge

 

SURGE TYPE CLASSIFICATION

A unified review of all test runs reveals the existence of a range of different surge forms assessing the usually twofold classification as insufficient. In general, the height of surge will not be a function of the F_O number alone as the simplified approach of equ. 1 may reflect. In order to describe initial uniform flow conditions at least three parameters are necessary. Beside F_O and Q*, defining the relative discharge, h* as relative water depth is considered to account for differences of frictional effects. The strong deformation of the surge in the longitudinal direction additionally demands the introduction of a length parameter L*. Moreover, expecting that the duration of the gate operation T may influence the surge formation too, a further dimensionless time number T* is applied. Regarding similarity principles the

 

individual terms write , , and

 

in which v_O denotes the initial mean flow velocity, B the channel width, g the acceleration due to gravity, h_O the initial water depth, k the equivalent wall roughness, L the distance from the gate and T the closing time of the gate. As a whole, the relative surge depth z* will be a function of

 

Eq. 4

 

In Fig. 2 the development of the surge wave along the channel is characterised. Various relevant surge types are to be considered. At the vicinity of the gate the first visible elevation of water table takes on a steep front for short time operations (SS) and a substantially flatter front with increasing closing time (FS). While propagating, the surge deforms with growing distance. The kind of deformation is additionally influenced by the F_O and h* number. For high discharges, short time closing and F_O > 0,7, a ventilated surge (VS) without any oscillations emerges, Fig. 2a. Smaller discharges at longer closing times are also able to produce a ventilated surge (OVS), however the main elevation is strongly superposed by oscillations, which dominate the total wave behaviour. The OVS-type is quite different in character compared to the first case, Fig.2b. With increasing distance from the gate as well as decreasing F_O number the ventilation vanishes and a solely oscillating surge wave (OS) appears. With regard to the closing time various subtypes can be distinguished, which are of no practical relevance. Within a certain range of flow conditions a primary OS-wave propagating along the channel can turn into the OVS and return into the original OS-state, Fig 2b. Due to frictional effects all surges transform by the time to the OS-state, Fig. 2c and subsequently to a deformed FS-type. Fig. 3 tries to quantify the thresholds between the classified surges in function of varying closing time. The surge development is traced for two constant discharges Q* and three F_O conditions. For F_O= 0,7, the VS-Type only covers a small zone for very short closing times T*. Looking at longer T*, two thresholds regarding the transition from the OS to the OVS type can be separated. While the lower line characterises the beginning of ventilation the upper line identifies the decay into the OS state. With rising discharge the thresholds shift to the right side and upwards. On the other hand decreasing F_O numbers move the thresholds downwards and to the left side, Fig. 3b and 3c. If F_O < 0,38 the transitional regime nearly disappears and the OS-type predominates. Under this condition the closing time does not influence the kind of surge anymore, yet the height of the oscillating surge.

 

Fig.2 observed surge types

 

Fig.3 thresholds of relevant surge states

 

SURGE HEIGHT CHARACTERISTICS

The development of a surge is always dominated by its first peak. Only at short closing times the first peak forms the maximum surge amplitude. The longer the closing time the smaller the first peak becomes. Fig. 4 displays the development of a surge along the channel for three different closing times. Also shown is the theoretical surge depth z_S*. Referring to the Favre criterion Eq. 2, a complete ventilation of the surge has to be expected. This result is in contrast to the observations in the test flume. Only for T* < 4 an OVS-type prevails along the channel reach. At a longer T*, the ventilated surge exclusively develops at a certain distance from the gate, as soon as the magnitude of z₁/h_O exceeds 0,6. Therefore the Favre criterion is not completely sufficient and has to be extended considering further parameters according to the diagrams of Fig. 3.

Of practical importance is the development of the maximum surge amplitude z_max especially in the OS domain. To prove the relevance of the theoretical surge height z_S, a ratio of z_max/z_S is applied. Fig. 5 compares the conditions of two constant discharges at a particular distance from the gate. In this diagram the existence of a critical closing time producing the highest surge amplitude becomes clearly evident. Shorter and longer closing times result in smaller surges. The highest amplitude occurs at a particular distance L _crit along the channel.

Referring to the critical time and the critical distance an enveloping curve of the highest values of z_max/z_S along the channel can be drawn, Fig. 6. Although limited by the range of the investigated data, the diagram offers a first information about the extend of under- and overestimation of surge height when applying the theoretically computed surge depth z_S.

 

Fig.4 development of the first surge peak along the channel

 

Fig. 5 relative maximum surge peak versus closing time of the gate at a particular distance

 

Fig.6 highest surge level formation along the channel with respect to the critical closing time

 

CONCLUSIONS

The experimental results convincingly confirm an appreciable influence of the duration of the gate closing on the surge development.

the closing time not only influences the development of specific types of surges but also the maximum surge height along the channel reach. There is a critical closing time T_crit which can produce a maximum surge level. The elevation ratio z_max/h_O at a certain site and a given discharge varies with the F_O and h* number of flow. Directly correlated with the closing time is the longitudinal development of the surge.

surge types split up into various subtypes. Particularly in the case of the ventilated surge, the classification has to consider the effect of superposing oscillations. In principle any ventilated surge is to be classified as a temporary phenomenon. Due to the frictional losses, at last these surges degenerates into the type of an oscillating surge.

the highest surge depths appear in the domain of the oscillating surge. Considering critical closure times enveloping curves for the maximum surge depth can be established. With regard to the highest discharge used in the experiments, the maximum wave elevation ratio (z_max/z_S)_max reaches 1,4 at F_O @ 0,3, which is slightly below the theoretical factor of Eq. 3. With an increasing F_O number the ratio (z_max/z_S)_max decreases significantly, dropping even below the value of 1. According to this result positive upstream surges are significantly smaller than positive downstream surges, for which Treske (1994) observed elevation ratios up to 2.

 

REFERENCES

Favre H.: Etude theorique et experimentale des Ondes de Translation dans canaux decouverts, Dunod Paris, 1935

Martin H.: Plötzlich veränderliche instationäre Strömungen in offenen Gerinnen, Technische Hydromechanik, Band 2 ed. G. Bollrich, VEB Verlag für Bauwesen Berlin , 1990

Treske A.: Favre Waves in Open Channels - Experimental Studies, Joumal of Hydraulic Research, Vol. 32, No. 3, 1994

Viehweider J.: Experimentelle Bestimmung des Einflusses von Durchflußänderungen auf die Schwallhöhenausbildung in Gerinnen, diploma thesis, Institut für Wasserbau, Innsbruck University, 1997